arXiv subjects

Sandro Frigio

Publications and source records attributed to Sandro Frigio.

2 recordsLinked to original sources

arXiv2017

On the blow-up of some complex solutions of the 3-d Navier-Stokes Equations: Theoretical Predictions and Computer simulations

We consider some complex-valued solutions of the Navier-Stokes equations in $R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the "fluid" remains quiet.

math-ph↗

arXiv2017

Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations

We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".

physics.flu-dyn↗